Is it possible to dock the annotation layers window?
The Annotation layers can also be found in the View Panel in the Right hand side panels. (Toggle with N)
You don't need to be using the Annotate tool to access it.
To keep it in place, right click on the sub-panel header and choose Pin. You can also use SHIFT + Left Mouse. Notice the Pin icon in the top right.
Click and drag the 8 dots in the top right of the sub-panel to rearrange it on top of all the others. That way it's always on top of whatever Panel you are in.